This insignia is one of the most common shoulder sleeve insignia or patches worn during the Second World War, according to war historian Dr. Howard G. Lanham. He explains:
"It was officially adopted on
19 March 1942 as the patch of the Army Air Forces. In a sense it was a
"default" patch that a member of the Army Air Force would wear, who did
not have a more specific patch authorized; such as that of the 8th Air
Force, for example. It was generally worn on the left shoulder of the
service coat or shirt."
Lanham provides additional examples of some of the manufacture
styles on his website: Variations of Shoulder Sleeve Insignia, Second World War
Lanham continues: "When
the U.S. Air Force was organized in 1949 they dropped the use of this
patch, but it was still something that might have been worn by WWII
veterans still on active duty with the Army -- as a former unit patch on
the right sleeve. If you have any other questions that I can help with
feel free to write."